Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-26T13:40:32.670Z Has data issue: false hasContentIssue false

Cobordism of theta curves in S3

Published online by Cambridge University Press:  24 October 2008

Kouki Taniyama
Affiliation:
Department of Mathematics, School of Science and Engineering, Waseda University, Ohkubo, Shinjuku, Tokyo, 169, Japan

Abstract

In this paper we show that the cobordism classes of theta curves in S3 form a group under vertex connected sum. We investigate this group by means of knot cobordism and link cobordism.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Cochran, T. D.. Concordance invariance of coefficients of Con way's link polynomial. Invent. Math. 82 (1985), 527541.CrossRefGoogle Scholar
[2]Cochran, T. D.. Geometric invariants of link cobordism. Comment. Math. Helv. 60 (1985), 291311.CrossRefGoogle Scholar
[3]Jin, G. T.. On Kojima's η-function of links. In Differential Topology (Siegen.1987), Lecture Notes in Math. vol. 1350 (Springer-Verlag, 1988), pp. 1430.CrossRefGoogle Scholar
[4]Kauffman, L. H.. On Knots. Ann. of Math. Studies no. 115 (Princeton Univ. Press, 1987).Google Scholar
[5]Kawauchi, A.. On the Alexander polynomials of cobordant links. Osaka J. Math. 15 (1978), 151159.Google Scholar
[6]Kinoshita, S.. On elementary ideals of polyhedra in the 3-sphere. Pacific J. Math. 42 (1972), 8998.CrossRefGoogle Scholar
[7]Kinoshita, S.. On θn-curves in R 3 and their constituent knots. In Topology and Computer Science (editor Suzuki, S.), (Kinokuniya, 1987), pp. 211216.Google Scholar
[8]Kojima, S. and Yamasaki, M.. Some new invariants of links. Invent. Math. 54 (1979), 213228.CrossRefGoogle Scholar
[9]Nakagawa, Y.. On the Alexander polynomials of slice links. Osaka J. Math. 15 (1978), 161182.Google Scholar
[10]Rolfsen, D.. A surgical view of Alexander's polynomial. In Oeometric Topology, Lecture Notes in Math. vol. 438 (Springer-Verlag, 1974), pp. 415423.CrossRefGoogle Scholar
[11]Sakuma, M.. On strongly invertible knots. In Algebraic and Topological Theories, (editors Nagata, M. et al. ), (Kinokuniya, 1985), pp. 176196.Google Scholar
[12]Sato, N.. Cobordisms of semi-boundary links. Topology Appl. 18 (1984), 225234.CrossRefGoogle Scholar
[13]Wolcott, K.. The knotting of theta curves and other graphs in S 3. In Geometry and Topology (editors McCrory, C. and Shifrin, T.), (Marcel Dekker, 1987), pp. 325346.Google Scholar